Homomorphisms of product semigroups
type: Item
instance of: scholarly article
title: Homomorphisms of product semigroups
zbMATH Open document ID: 1484.39027
published in: Results in Mathematics
publication date: 2022-02-03T00:00:00Z
review text: Let \(S_1, S_2, \ldots, S_N\) and \(R\) denote semigroups, and \(F : S_1 \times \cdots \times S_N \to R\) be a homomorphism. The author finds sufficient conditions for existence and uniqueness of decompositions of \(F\) as \(F = F_1 \otimes \cdots \otimes F_N\), where \(F_n : S_n \to R\) is a homomorphism for \(n = 1, \ldots, N\). Explicit formulas and properties of the composing homomorphisms \(F_1, \ldots, F_N\) are given. He also applies the theory to some interesting examples. In addition, he studies additive and multiplicative functions on a product of subsemigroups of \(\mathbb{N}\).
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 20M30
Mathematics Subject Classification ID: 39B32
zbMATH DE Number: 7468845
zbMATH Keywords: semigroup
zbMATH Keywords: product semigroup
zbMATH Keywords: decomposition
zbMATH Keywords: homomorphism
author: Henrik Stetkær
MaRDI profile type: Publication
full work available at URL: s00025-022-01603-w
OpenAlex ID: W4205304505
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DOI: 10.1007/S00025-022-01603-W
description: scientific article; zbMATH DE number 7468845